A novel feature extraction technique is presented in this paper for an offline handwritten Gurmukhi character recognition system. Handwritten character recognition is a complex task because of various writing styles of different individuals. To select a set of features is an important step for implementing a handwriting recognition system. In this work, we have extracted various topological features, namely, peak-extent features, shadow features and centroid features. A new feature set is also proposed by using horizontal peak extent features and the vertical peak extent features. For classification, we have used k-NN and Linear-SVM classifiers. In view of learning and simplification capabilities of multi layer perceptrons (MLPs), MLPs based pattern classifier is also used for classification. In the present work, we have taken 7,000 samples of offline handwritten Gurmukhi characters for training and testing. Proposed system achieves a maximum recognition accuracy of 95.62% using SVM with linear kernel classifier. By using k-NN and MLPs, a maximum recognition accuracy of 95.48% and 94.74%, respectively, has been achieved with five-fold cross validation.